Assignment 1

Instructions to Solve Assignments

The purpose of the assignments is to give students hands on practice. It is expected that students will solve assignments themselves. The Following rules that will apply during the evaluation of the assignment.

Cheating from any source will result in zero marks in the assignment.

Any student found cheating in any two of the assignments submitted during the course will be awarded

“F” grade in the course.

No assignment after the due date will be accepted.

Answer the following questions in your own words. Plagiarism will be checked for each question. Marks will be awarded on the basis of the answer and plagiarism report.

Question No.1 (15 Marks)

Prove with the help of logical equivalence that the given proposition is a tautology. (p Λ q) v (~ p v ~( pq ))

Note: Show all the steps to get full marks

Question 2 (25 Marks)

Show by mathematical induction that any amount in cents ≥ n0 cents can be obtained using 8 cents and 9 cents coins only.

Note: First you will need to calculate n0.

Question No.3

Consider the recurrence

tn =n

(20) Marks

tn = 4tn-1 -11tn-2

Find general solution of the recurrence above.

-6tn-3

otherwise

ifn=0,1,2

Assignment 1

Instructions to Solve Assignments

The purpose of the assignments is to give students hands on practice. It is expected that students will solve assignments themselves. The Following rules that will apply during the evaluation of the assignment.

Cheating from any source will result in zero marks in the assignment.

Any student found cheating in any two of the assignments submitted during the course will be awarded

“F” grade in the course.

No assignment after the due date will be accepted.

Answer the following questions in your own words. Plagiarism will be checked for each question. Marks will be awarded on the basis of the answer and plagiarism report.

Question No.1 (15 Marks)

Prove with the help of logical equivalence that the given proposition is a tautology. (p Λ q) v (~ p v ~( pq ))

Note: Show all the steps to get full marks

Question 2 (25 Marks)

Show by mathematical induction that any amount in cents ≥ n0 cents can be obtained using 8 cents and 9 cents coins only.

Note: First you will need to calculate n0.

Question No.3

Consider the recurrence

tn =n

(20) Marks

tn = 4tn-1 -11tn-2

Find general solution of the recurrence above.

-6tn-3

otherwise

ifn=0,1,2

**Q. 2 Solution:**

**Q. 3 Solution:**